1823.] the Barometer to the Measurement of Heigftts, 10& 



1 have collected a number of observations running through a 

 scale of nearly 21,000 feet of elevation, and at temperatures 

 varying from — 1° to -f 28°. Now whatever law of decrease 

 we may have deduced from theory, from the abstract constitu- 

 tion of the atmosphere, &c. it will be impossible to make it agree 

 with these results. Slow and rapid diminutions of temperature 

 accompany indifferently both great and small elevations; we 

 find them taking place indiscriminately in the higher, middle, and 

 lower regions of the atmosphere; and at all degrees of heat and 

 cold. Yet these are good observations, and have furnished in 

 general very exact measurements, and many of them con- 

 firmed by geometrical determination. And they are moreover 

 the same sort of observations which we commonly make, and fo^ 

 which our barometric formulse are constructed. The measure- 

 ments are found accurate, because the thermometer consulted 

 at the lower station has eliminated an unknown quantity to 

 which no theoretical considerations could have assigned a deter- 

 minate value. A corresponding observation at the base of the 

 column is a fixed point of departure; the extremes of the temper- 

 ature being once known, correct the calculation ; and although 

 the decrease of temperature generally undergoes, in the same 

 column of air, irregularities occasioned by a multitude of acci- 

 dental causes, which by turns retard and accelerate it, and is 

 sometimes inverted ; yet an arithmetical mean taken between 

 the extreme temperatures so well covers these irregularities, that 

 the exactness of the measurements is not at all affected. 



It may sometimes happen that we have not corresponding 

 observations ; and when we carry a barometer, we are desirous 

 of deducing at once from it nearly the absolute elevation of the 

 place. The expedient hitherto most commonly adopted has 

 been to compare the observed height of the barometer with its 

 mean height at the level of the sea ; but in this method there is 

 always an inherent fault : we compare an insulated observation 

 with the mean of a great number of observations. The compa- 

 rison will only be just in the single case when the barometer 

 happens accidentally to be precisely at its mean height; iii 

 general, it may be considerably above or below it ; there is then 

 only one chance in favour of the accuracy of the measurement; 

 that is, by allowing for the diminution of temperature according 

 to the approximate elevation, and the error in this correction 

 happening to compensate the former : if, however, the two 

 errors instead of compensating each other, accumulate, the appa- 

 rent amelioration of the calculation will have no other effect than 

 to increase the inaccuracy. We may, however, proceed thus : 

 Suppose themedn height of the barometer at the level of the sea 

 to be 30*03437 itiches at a temperature of 12*5°, a supposition 

 adopted by most philosophers from the observations of Sir G. 

 Shuckburgh. I commence by reducing my observation to the 



